diff --git a/changelog.d/9795-string-code-point-at-dispatch.md b/changelog.d/9795-string-code-point-at-dispatch.md
new file mode 100644
index 0000000000..04cde8e0c0
--- /dev/null
+++ b/changelog.d/9795-string-code-point-at-dispatch.md
@@ -0,0 +1,12 @@
+### Runtime
+
+- perf(runtime): `String.prototype.codePointAt` is answered by the native
+  string-method dispatch instead of falling through to the primitive-method
+  fallback. It had a prototype thunk but no dispatch arm, so every call
+  resolved `globalThis.String.prototype.codePointAt`, cloned that closure to
+  rebind `this`, and — the thunk not being registered strict — ran `ToObject`
+  on the receiver, minting a `String` wrapper with an own index property per
+  UTF-16 code unit. Grapheme-aware text measurement calls it once per
+  character: on the compiled claude-code TUI it was the only method name
+  reaching the fallback, at 99,008 calls and 99,008 wrappers per 400-character
+  streamed reply (`PERRY_GC_DIAG=1`, `[gc-primitive-dispatch]`).
diff --git a/crates/perry-runtime/src/object/native_call_method.rs b/crates/perry-runtime/src/object/native_call_method.rs
index f05a2285a6..c7452709a7 100644
--- a/crates/perry-runtime/src/object/native_call_method.rs
+++ b/crates/perry-runtime/src/object/native_call_method.rs
@@ -18,6 +18,8 @@ mod primitive_methods;
 mod proto_dispatch;
 mod string_methods;
 
+#[cfg(test)]
+mod code_point_at_dispatch_tests;
 #[cfg(test)]
 mod dispatch_arg_coercion_tests;
 #[cfg(test)]
diff --git a/crates/perry-runtime/src/object/native_call_method/code_point_at_dispatch_tests.rs b/crates/perry-runtime/src/object/native_call_method/code_point_at_dispatch_tests.rs
new file mode 100644
index 0000000000..e1ce0b8cfc
--- /dev/null
+++ b/crates/perry-runtime/src/object/native_call_method/code_point_at_dispatch_tests.rs
@@ -0,0 +1,80 @@
+//! #9761: `String.prototype.codePointAt` must be answered by the native
+//! string-method dispatch, not by the primitive-method FALLBACK.
+//!
+//! The fallback (`call_primitive_builtin_prototype_method`) resolves
+//! `globalThis.String.prototype[<name>]`, clones that closure to rebind `this`,
+//! and — because the resolved thunk is not registered strict — runs `ToObject`
+//! on the receiver, minting a `String` wrapper with an own index property per
+//! UTF-16 code unit. `codePointAt` had a prototype thunk but no dispatch arm,
+//! and grapheme-aware text measurement calls it once per character: on the
+//! compiled claude-code TUI it was the ONLY name reaching the fallback, at
+//! 99,008 calls (and 99,008 wrappers) per 400-character streamed reply.
+//!
+//! The assertion is the wrapper count, not the return value: a test that only
+//! checked the answer would pass with the arm deleted, because the fallback
+//! computes the same number — expensively. `BOXED_PRIMITIVE_PAYLOADS` gains one
+//! entry per wrapper, so "no new boxed primitives" is exactly "the fallback did
+//! not run".
+
+use crate::value::JSValue;
+
+unsafe fn call_string_method(receiver: &str, method: &str, args: &[f64]) -> f64 {
+    let s = crate::string::js_string_from_bytes(receiver.as_ptr(), receiver.len() as u32);
+    let recv = f64::from_bits(JSValue::string_ptr(s).bits());
+    super::js_native_call_method(
+        recv,
+        method.as_ptr() as *const i8,
+        method.len(),
+        if args.is_empty() {
+            std::ptr::null()
+        } else {
+            args.as_ptr()
+        },
+        args.len(),
+    )
+}
+
+#[test]
+fn code_point_at_dispatches_natively_and_boxes_no_receiver() {
+    unsafe {
+        // Warm anything the first dispatch installs, so the delta below is the
+        // method call itself and not one-time globalThis population.
+        let _ = call_string_method("ab", "charCodeAt", &[0.0]);
+        let before = crate::builtins::test_boxed_primitive_payload_count();
+
+        let cp = call_string_method("a", "codePointAt", &[0.0]);
+        assert_eq!(cp, 97.0, "codePointAt(0) of \"a\"");
+        let astral = call_string_method("\u{1F600}b", "codePointAt", &[0.0]);
+        assert_eq!(astral, 128512.0, "an astral pair is one code point");
+        let past_end = call_string_method("a", "codePointAt", &[5.0]);
+        assert!(
+            JSValue::from_bits(past_end.to_bits()).is_undefined(),
+            "out of range is undefined"
+        );
+
+        assert_eq!(
+            crate::builtins::test_boxed_primitive_payload_count(),
+            before,
+            "the native arm must not mint a String wrapper; a non-zero delta \
+             means the call fell through to the primitive-method fallback"
+        );
+    }
+}
+
+/// Positive control for the assertion above: the counter must be able to move,
+/// or "no new boxed primitives" proves nothing. Minting the wrapper the
+/// fallback would have minted is the direct, environment-independent form —
+/// a second dispatch through a name without a native arm cannot serve as the
+/// control here, because the unit-test thread has no populated `globalThis`
+/// and the fallback returns before it boxes.
+#[test]
+fn the_wrapper_counter_moves_when_a_receiver_is_boxed() {
+    let before = crate::builtins::test_boxed_primitive_payload_count();
+    let s = crate::string::js_string_from_bytes(b"abc".as_ptr(), 3);
+    let value = f64::from_bits(JSValue::string_ptr(s).bits());
+    let _wrapper = crate::builtins::js_boxed_string_new(value, 1);
+    assert!(
+        crate::builtins::test_boxed_primitive_payload_count() > before,
+        "if this cannot move, the codePointAt assertion above is vacuous"
+    );
+}
diff --git a/crates/perry-runtime/src/object/native_call_method/string_methods.rs b/crates/perry-runtime/src/object/native_call_method/string_methods.rs
index cae30b6a76..d6213dee14 100644
--- a/crates/perry-runtime/src/object/native_call_method/string_methods.rs
+++ b/crates/perry-runtime/src/object/native_call_method/string_methods.rs
@@ -136,6 +136,20 @@ pub(super) unsafe fn dispatch_string(
                 "charCodeAt" => {
                     return Some(crate::string::js_string_char_code_at(s_ptr, arg_i32(0)));
                 }
+                // #9761: `codePointAt` had a `String.prototype` thunk but no
+                // arm here, so it was the ONE method name the compiled
+                // claude-code TUI drove into the primitive-method FALLBACK:
+                // 99,008 calls per 400-character reply, each of which looked
+                // `globalThis.String` up, cloned the prototype closure to
+                // rebind `this`, and — because the callee is sloppy — ran
+                // `ToObject` on the receiver, minting a `String` wrapper with
+                // its own index property. Grapheme-aware text measurement
+                // calls it once per character, so a missing arm here is a
+                // per-character wrapper. It is the sibling of `charCodeAt`
+                // one line up and reads the same receiver the same way.
+                "codePointAt" => {
+                    return Some(crate::string::js_string_code_point_at(s_ptr, arg_i32(0)));
+                }
                 "slice" => {
                     // Coerce args first (`arg_i32` may run user `valueOf` and move
                     // the receiver under GC), then re-fetch the rooted receiver.